A Novel Molecular Communication System
Using Acids, Bases and Hydrogen Ions
Nariman Farsad, Member, IEEE, and Andrea Goldsmith, Fellow, IEEE,
arXiv:1511.08957v1 [cs.ET] 29 Nov 2015
Department of Electrical Engineering, Stanford University, CA, USA.
Abstract—Concentration modulation, whereby information is
encoded in the concentration level of chemicals, is considered.
One of the main challenges with such systems is the limited
control the transmitter has on the concentration level at the
receiver. For example, concentration cannot be directly decreased
by the transmitter, and the decrease in concentration over time
occurs solely due to transport mechanisms such as diffusion.
This can result in inter-symbol interference (ISI), which can have
degrading effects on performance. In this work, a new and novel
scheme is proposed that uses the transmission of acids, bases,
and the concentration of hydrogen ions for carrying information.
By employing this technique, the concentration of hydrogen ions
at the receiver can be both increased and decreased through the
sender’s transmissions. This enables novel ISI mitigation schemes
as well as the possibility to form a wider array of signal patterns
at the receiver.
Index Terms—Molecular Communication, Chemical Reactions,
Chemical Signaling, pH Signaling
I. I NTRODUCTION
M
OLECULAR communication is a new and emerging
field, where information is conveyed through chemical
signals [1]. In this paradigm, the transmitter releases tiny
particles, where information is modulated onto the chemical
properties of these particles. The particles then propagate
through the medium until they arrive at the receiver, where
the chemical signal is demodulated and the information is decoded. Although there are many different forms of transport in
molecular communication (e.g. active transport [2]), the most
common propagation mechanism considered in the literature
is diffusion-based transport with and without flow between the
transmitter and receiver [1].
Different modulation schemes have been proposed for
molecular communication including: concentration modulation [3], type-based modulation [4], and timing of release
modulation [5]; a summary of some of these techniques
can be found in [6]. Between these modulation schemes,
concentration modulation has received the most attention in
the literature, since it can be detected with relative ease. For
example, in [7], a simple and inexpensive over-the-air tabletop
demonstrator was developed for a concentration-modulated
molecular diffusion channel with flow.
One of the issues with concentration-modulated diffusionbased molecular communication is that the concentration at
the receiver increases with consecutive transmissions and
only decreases as the particles diffuse away. Since diffusion
can be a slow process, this will result in significant intersymbol interference (ISI) [8]. This is evident in the long
tails associated with the system’s impulse response [5]. Some
previous works have proposed ISI mitigation techniques, such
as the use of enzymes for destroying the chemicals that remain
in the channel from previous transmissions [9]. However, in
these techniques the transmitter does not have control over the
chemical reactions in the channel, nor can it actively decrease
the concentration at the receiver.
In this work, a new and novel signaling scheme using acids,
bases, and the concentration of hydrogen ions is proposed. In
this scheme, the transmitter can release either a strong acid
or a strong base. The strong acids and bases dissociate almost
completely in aqueous solutions (i.e. solutions where water
is the solvent) to form hydrogen ions and hydroxide ions,
respectively [10]. Moreover, if used in low concentrations,
strong acids and bases are not corrosive or destructive to the
transmitter and receiver. Because of the water autoionization
reaction, which will be explained in detail in this paper,
concentration of hydrogen ions and hydroxide ions are almost
always non-zero, and the product of concentration of both ions
is a constant. Therefore, an increase in the concentration of one
species results in a proportional decrease in the concentration
of the other species. The received signal at the destination is
obtained by measuring the pH level, where pH is the negative
log of the concentration of hydrogen ions.
There are multiple benefits to using this scheme. First, for
detection at the receiver, pH sensors are available at microscales and macro-scales, which makes this technique practical.
Second, the concentration of hydrogen ions at the receiver can
be directly increased and decreased by the transmitter. Third,
a wider array of signal patterns can be formed at the receiver
using this extra degree of freedom, which could then be used
in different applications such as to generate control signals
for synthetic biological devices, or as non-binary modulation
schemes. For example, it was recently shown that pH signals
could be used to control the motion direction of bacteria [11].
In this work we focus on ISI mitigation, and show that the
proposed system could significantly reduce the ISI.
The rest of this paper is organized as follows. In Section
II the chemical reactions between the strong acids, strong
bases, and hydrogen ions are presented. Then, in Section III
the system model for this channel is presented. The system
response to an impulse of acid or base is studied in Section
IV. An ISI mitigation technique is proposed in Section V,
through consecutive transmission of an acid impulse followed
by a base impulse. The paper ends with concluding remarks
and future work in Section VI.
II. ACIDS , BASES AND P H S CALE
In an aqueous environment, one important process is
the autoionozation of water [10]. In this process, two water molecules are combined to generate a hydronium ion
(H3 O+ )and a hydroxide ion (OH– ). The equation for this
reaction is shown below:
−
+
−
*
2 H2 O −
)
−
− H3 O (aq) + OH (aq).
(1)
Note that alternatively, in some texts, this reaction equation is
simplified and written as
−
+
−−
*
H2 O )
−
− H (aq) + OH (aq).
(2)
In this paper, the two equations and hence ions H+ (i.e. hydrogen ion) and H3 O+ are used interchangeable. The equilibrium
constant for the autoionozation reaction is given by [10]
−
+
kw = [H ][OH ],
(3)
where the notation [.] is used to indicate the concentration of
ions and molecules. For water at 25◦ C, kw = 10−14 . For pure
water, since there are no other sources for ion formation, the
concentration of both ions are equal and therefore we have
+
−
[H ] = [OH ] = 10−7 M,
(4)
where M, called molar, is units of concentration and represents
the number of moles per every liter of solution (i.e. mol/L).
The molar concentration of a chemical can be related to the
number of molecules of that chemical using the relation M =
N
na L , where N is the number of molecules, na is Avogadro’s
number, and L is the volume of solution. Therefore, the
number of ions in every liter would be 10−7 × 6.022 × 1023 =
6.022×1016 , where the second number is Avogadro’s constant.
The pH measure is the negative log scale of the concentration of hydrogen ions H+ (or H3 O+ ). Therefore, the pH of
pure water at 25◦ C is
+
pH = − log([H ]) = 7.
(5)
Similarly, pOH represents the negative log scale of the
concentration of hydroxide ions OH– . At 25◦ C we have
pH+pOH=pkw =14 (pkw is the negative log of kw ). At this
temperature the solution is neutral if pH = 7, acidic if pH < 7
(i.e. the concentration of hydronium/hydrogen ions is more
than the concentration of hydroxide ions), and basic if pH > 7
(i.e. the concentration of hydroxide ions is more than the
concentration of hydronium/hydrogen ions).
According to the Brønsted-Lowry definition of acids and
bases, an acid is a proton donor, while a base is a proton
acceptor [10]1 . Notice that according to this definition, water
is both an acid and a base, since in (1), one water molecule
donates a proton while the other one accepts a proton.
An acid or a base is called a strong acid or a strong base
if it almost completely dissociates in aqueous solutions (i.e.
1 Although we use the Brønsted-Lowry definition of acids and bases in this
paper, there are also the Arrhenius and the Lewis definitions of acids and
bases. The Brønsted-Lowry definition, which is used in most textbooks, lends
itself better to our analysis.
solutions where water is the solvent). Note that a strong acid or
base does not necessarily result in an extremely low or high pH
value. If the strong acid or base is used in low concentrations,
the pH value of the solution would be close to the neutral
pH, and the solution would not be corrosive or destructive.
The dissociation reactions for strong acids and bases can be
represented by the following chemical equations
AH(aq) + H2 O(l) −−→ H3 O+ (aq) + A− (aq),
(6)
B(aq) + H2 O(l) −−→ BH+ (aq) + OH− (aq),
(7)
where AH is a strong acid and B is a strong base. In this work,
the acid-base interaction that combines the A− and BH+ to
form a salt is ignored, since it does not have an effect on the
concentration of hydrogen ions and the pH.
If the quantity of the strong acid or base is small compared
to the quantity of water, the dissociation happens almost
instantly [12]. Using (1) and (6) together, it can be seen that the
H+ ion concentration increases, and the OH– ion concentration
decreases as a strong acid is injected in the water. Similarly,
using (1) and (7) together, it is observed that the concentration
of OH– ions increases and the H+ ion concentration decreases
as a strong base is dropped in the water. For example, if
6.022 × 1022 molecules of a strong acid are dropped in a
one liter water container, at steady state, the concentration of
hydrogen ions would be [H+ ] = 0.1 M, the concentration of
hydroxide ions would be [H+ ] = 10−13 M, and the pH of the
solution would be 1.
III. S YSTEM M ODEL
The system that is considered in this paper consists of
a molecular communication transmitter that can release two
different types of chemicals: a strong acid or a strong base.
Note that a strong acid or base does not necessarily result
in a very low or high pH value that could be destructive. If
they are used in low concentrations, the pH levels could be
kept closer to the neutral pH. Figure 1 depicts the proposed
communication system. It is assumed that the transmitter can
transmit both chemicals simultaneously in any concentration.
It is also assumed that the distance between the “nozzles” that
release the acid and base is small enough such that we can
assume both chemicals are released from a single nozzle. The
coordinate system that is used to study this communication
channel is assumed to be centered at the tip of the nozzle, and
the transmitter is a point source at this location.
As was explained in the previous section, the strong acids
and bases almost completely dissociate in water to form hydrogen (H+ ) or hydroxide (OH− ) ions. This process happens
very rapidly within a few microseconds [12]. Therefore, in this
work it is assumed that transmitting a strong acid is equivalent
to releasing hydrogen ions and transmitting a strong base
is equivalent to releasing hydroxide ions. The released ions
propagate through convection-diffusion (or potentially pure
diffusion) until they arrive at the receiver. The receiver would
then use a pH meter to measure the pH level and detect the
concentration of hydrogen ions.
Acid Transmitter
H+
pH Sensor
Tx
Rx
Base Transmitter
Fig. 1.
OH-
Depiction of the proposed communication system.
The only reaction involving the hydrogen and hydroxide
ions in the channel is the water autoionization reaction given
in (2). Because the communication environment is inside a
fluid, where the main solution is water, it can be assumed
that there are always water molecules everywhere ready to
dissociate. Therefore, reaction (2) can be written as
kf
−−
*
H+ (aq) + OH− (aq) )
−
−∅
(8)
kr
where kf and kr are the forward and reverse reaction rates,
respectively. At 25◦ C the forward reaction rate for combination of H+ and OH− ions is kf = 1.4 × 1011 1/Ms [13]. The
water dissociates into these ions at the rate 2.5×10−5 1/s [13].
Since the molar concentration of water is 55.5 M, the reverse
reaction rate is kr = 2.5 × 10−5 × 55.5 = 1.4 × 10−3 M/s,
which represents the rate at which the two ions are generated
[13]. Note that the forward reaction rate is much larger than
the reverse reaction rate, which is the reason for very low ion
concentrations of 10−7 M at equilibrium compared to 55.5 M
of water.
Let CH (x, t) and COH (x, t) represent the average spatiotemporal concentration of H+ and OH− ions, respectively.
The average behavior of the transport system can be represented using a system of partial differential equations as
∂CH
= DH ∇2 CH − ∇.(vCH ) − kf CH COH + kr
(9)
∂t
∂COH
= DOH ∇2 COH − ∇.(vCOH ) − kf CH COH + kr ,
∂t
(10)
where DH and DOH are the diffusion coefficients of H+
and OH− ions in water, and v is the velocity field. For pure
diffusion the velocity field is assumed to be zero everywhere
in the channel. It is assumed that dimensions of the channel
environment are much larger than the separation distance between the transmitter and receiver. Therefore, infinite boundary
conditions are assumed (i.e. CH (x = ∞, t) = COH (x =
∞, t) = 0).
The transmission process can be modeled by adjusting the
initial conditions. Two scenarios are possible: only hydrogen
ions (i.e. a strong acid) are released, or only hydroxide ions
are released (i.e. a strong base). Note that if hydrogen ions
and hydroxide ions (i.e. strong acid and base) are released
simultaneously, because the forward reaction rate kf is very
large, they immediately combine and neutralize to form water
molecules. Therefore, the net effect would be one of the
two scenarios mentioned earlier depending on the amount
of hydrogen and hydroxide ions that were released. The two
transmission processes can be represented by initial conditions
(
init
CH (x, t = 0) = NH δ(x) + CH
(x)
Tx releases H+
init
COH (x, t = 0) = COH
(x)
(11)
(
init
CH (x, t = 0) = CH (x)
Tx releases OH−
init
COH (x, t = 0) = NOH δ(x) + COH
(x)
(12)
where the NH and NOH are the moles of hydrogen and
init
init
hydroxide ions released by the transmitter, CH
and COH
are
the initial concentration profiles of each ion in the channel,
and δ(.) is the vector form of the Dirac delta function. For
example, if x represents a three dimensional space, then
δ(x) = δ(x)δ(y)δ(z) where x, y and z are each axis of the
coordinate system. For the very first transmission, we assume
init
init
that CH
= COH
= 10−7 (i.e. only water is present in the
channel). This assumption is made to simplify our numerical
analysis, and can be relaxed without affecting the model.
Unfortunately, an analytical solution to the system of nonlinear partial differential equations in (9)–(10) with the given
boundary and initial conditions does not exist. Therefore, in
the next section, the solutions for the two initial conditions in
(11) and (12) are numerically evaluated and presented.
IV. S YSTEM R ESPONSE M ODEL AND E VALUATION
Solving a system of nonlinear partial differential equations
can be a computationally intensive task, especially when
considering 3-dimensional (3D) problems. Therefore, in this
initial work we consider a 1-dimensional (1D) space and
extend the results to higher dimensions in the future. To solve
the 1D system of equations in (9)–(10), the finite difference
method (FDM) is employed [14].
In FDM, time and space are discretized into finite intervals.
Let 0 ≤ t ≤ T and xa ≤ x ≤ xb be the time and spatial
interval over which a solution is required. In this work, it is
assumed that such intervals are divided into equal subintervals
of ∆t and ∆x, respectively. Let i and j be the index for each
subinterval. Then the approximate time corresponding to index
i is ti = i∆t and the approximate spatial coordinate for index
j is xj = xa + j∆x. Using this scheme, the partial derivatives
in (9)–(10) can be approximated as
C(xj , ti+1 ) − C(xj , ti )
∂C
(xj , ti ) ≈
(13)
∂t
∆t
∂2C
C(xj−1 , ti ) − 2C(xj , ti ) + C(xj+1 , ti )
(xj , ti ) ≈
∂x2
∆x2
(14)
∂C
C(xj+1 , ti ) − C(xj−1 , ti )
(xj , ti ) ≈
(15)
∂x
2∆x
Substituting these approximations in (9)–(10), it is possible
to find the concentrations at time index i + 1 from the
concentrations at time index i iteratively. The solution for
C(t) = N U (t)
(16)
with
U (t) =


1
(4πDt)d/2
0
2
exp − (`−vt)
t>0
4Dt
t≤0
,
(17)
where D is the diffusion coefficient of the particle, d ∈
{1, 2, 3} represents the spatial dimension of the system considered (i.e. 1D, 2D, and 3D), ` is the separation distance
between the transmitter and receiver, and v is the constant
velocity. Note that this is the solution of (9) or (10) without
the reaction terms. If we assume that there are no chemical
reactions (i.e. the hydrogen ions do not interact with any other
chemicals in the environment), (16) plus 10−7 would represent
the concentration of hydrogen ions at the receiver, and its
negative log the pH.
When we consider the reaction as well as the diffusion,
analytical expressions do not exist and only numerical evaluation is possible. For this case (9)–(10) are solved using FDM
for the initial condition (11). Note that instead of the Dirac
delta function in (11), a zero mean Gaussian pulse with a
standard deviation of 0.001 is used for numerical evaluations.
Let us now compare the approximation with no reactions, with
numerical solutions obtained using FDM. In the evaluations,
the diffusion coefficient of hydrogen ions is DH = 9.31×10−5
8
Hydrogen Ion Concentration at Receiver
the initial conditions is then obtained by setting the initial
concentrations at time index i = 0 according to (11) or (12).
In this section, a MATLAB implementation of this technique
is used to find a numerical solution of (9)–(10) and hence the
system response.
Although analytical solutions for the system model presented in this work do not exist, in the rest of this section,
approximate analytical expressions are presented for the case
when an acid impulse is transmitted and the case when a
base impulse is transmitter. For the acid transmission, it is
assumed that no reactions occur in the channel. This can
be a valid assumption, if for a single acid impulse the
initial concentration of hydrogen ions and hydroxide ions are
low compared to the amount of acid released. For the base
transmission, it is assumed that the reactions occur only at
the receiver and not in the channel. Again, this is a valid
assumption if the amount of base released by the transmitter
is much larger than the ions in the channel. Note that none of
these assumptions hold when considering multiple consecutive
transmissions. However, as will be shown in the next section,
they could be used to find numerical solutions using FDM for
two consecutive transmissions.
First, let us consider an acid impulse, where the number of
acid molecules released is much larger than the concentration
of ions in the channel. The approximate response is obtained
if it is assumed that there are no chemical interactions in the
channel. If the velocity is constant and in the direction from the
transmitter to the receiver, and there is a sudden impulse of N
moles of particles (i.e. N δ(x)) at time t = 0, the concentration
at the receiver as a function of time is given by
#10 -3
System Response to Acid Transmission
FDM Sol `=9007m, v=0
No Reac `=9007m, v=0
FDM Sol `=9007m, v=107m/s
No Reac `=9007m, v=107m/s
FDM Sol `=9007m, v=507m/s
No Reac `=9007m, v=507m/s
FDM Sol `=2mm, v=0
No Reac `=2mm, v=0
FDM Sol `=2mm, v=107m/s
No Reac `=2mm, v=107m/s
FDM Sol `=2mm, v=507m/s
No Reac `=2mm, v=507m/s
7
6
5
4
3
2
1
0
0
50
100
150
200
Time (s)
Fig. 2. The system response when the transmitter releases a strong acid (i.e.
hydrogen ions). The y-axis represent the concentration of hydrogen ions.
cm2 /s [15], and the diffusion coefficient of hydroxide ions is
DOH = 5.03 × 10−5 cm2 /s [15]. To represent the impulse
release of chemicals, it is assumed that 0.001 moles of that
chemical are released by the transmitter.
Figure 2 shows the results for three different flow velocities
and two different separation distances: flow velocities of 0, 10
µm/s, and 50 µm/s, at 900 µm and 2 mm. As can be seen in
the figure, the system response is the same for the case when
the reaction is considered versus the case when no reactions
are considered. This is because the initial concentration of
hydrogen and hydroxide ions in the channel are much lower
than the concentration of the ions released. However, this
will not hold when the initial concentration of hydrogen or
hydroxide ions in the channel are high.
Let us now consider the case when a strong base (i.e.
hydroxide ions) is released by the transmitter. In this case,
if the reactions are not considered, then the concentration of
hydrogen ions would be constant at 10−7 . Therefore, chemical
reactions must be included in any approximations. An approximate model in this case can be obtained if it is assumed
(R)
that the reactions occur only at the receiver. Let COH (t) be
the concentration of hydroxide ions that are released by the
(R)
transmitter and arrive at the receiver. The COH (t) can be analytically represented by (16). Since the channel environment
is essentially liquid water, (3) must always hold. Let x be
the number of water molecules that dissociate into hydrogen
and hydroxide ions. Note that in this case, the only source of
hydrogen ion is from water autoionization, and x represents
the concentration of hydrogen ions. From (3) we have
+
−
[H ][OH ] = kw
(R)
(x) x + COH (t) = kw
2
x +
(R)
COH (t)x
− kw = 0.
(18)
(19)
(20)
Solving this quadratic equation for x, we obtain an expression
for the concentration of hydrogen ions with respect to time:
q
2
(R)
(D)
−COH (t) +
COH (t) + 4kw
CH (t) =
.
(21)
2
System Response to Base Transmission
10 -8
10 -9
10 -10
10
-11
10
-12
0
50
100
System Response to Acid-Base Tx at 9007m
1
FDM Sol `=9007m, v=0
Reac @ Rx `=9007m, v=0
FDM Sol `=9007m, v=107m/s
Reac @ Rx `=9007m, v=107m/s
FDM Sol `=9007m, v=507m/s
Reac @ Rx `=9007m, v=507m/s
FDM Sol `=2mm, v=0
Reac @ Rx `=2mm, v=0
FDM Sol `=2mm, v=107m/s
Reac @ Rx `=2mm, v=107m/s
FDM Sol `=2mm, v=507m/s
Reac @ Rx `=2mm, v=507m/s
Normalized Hydrogen Ion Concentration
Hydrogen Ion Concentration at Receiver
10 -7
150
Time (s)
Fig. 3. The system response when the transmitter releases a strong base (i.e.
hydroxide ions). The y-axis represents the concentration on a log scale.
To evaluate the accuracy of this approximation, (9)–(10)
are solved for the initial condition (12) using FDM. All the
system parameters are the same as the case where a stong
acid was released by the transmitter and it is assumed that
0.001 moles of strong base are released. Figure 3 shows the
results. Unlike Figure 2, the y-axis in this plot represents
the concentration on a log scale. This is to highlight the
change in concentration of hydrogen ions which decreases
by several orders of magnitude. As expected, the increasing
concentration of hydroxide causes a decrease in concentration
of hydrogen ions. The approximation in (21) (i.e. when it is
assumed that the reactions occur only at the receiver) provides
a fairly accurate estimate of the concentration of hydrogen
ions. This is due to the fact that the initial concentrations of
hydrogen and hydroxide ions in the channel are low compared
to the concentration released by the transmitter. As will be
shown in the next section, this assumption does not hold when
consecutive transmissions are considered.
An important observation is that the concentration of hydrogen ions, and hence the pH level can both increase and
decrease depending on whether the transmitter releases an
acid or a base. Therefore, more complicated signals can be
transmitted to the receiver. For example, as will be shown in
the next section, consecutive transmissions could be used to
reduce the ISI significantly.
V. ISI M ITIGATION T HROUGH
C ONSECUTIVE T RANSMISSIONS
As was shown in the last section, one of the main benefits
of the proposed scheme is the ability of the transmitter to
control the increase and decrease of hydrogen ions at the
receiver through transmitting acids and bases. Although all
concentration-encoded molecular communication techniques
can control the increase of concentration at the receiver, there
have been no previous works that have reported a transmission
technique for decreasing the concentration at the receiver. For
example, the enzyme-based techniques proposed in [9] rely
on the enzymes in the channel, where the transmitter does not
have direct control over enzymes. Therefore, one of the most
0.9
0.8
0.7
0.6
0.5
0.4
0.3
Acid-Base Tx `=9007m, v=0
Acid Tx `=9007m, v=0
Acid-Base Tx `=9007m, v=107m/s
Acid Tx `=9007m, v=107m/s
Acid-Base Tx `=9007m, v=507m/s
Acid `=9007m, v=507m/s
0.2
0.1
0
0
50
100
150
200
Time (s)
Fig. 4. The system response at 900 µm when the transmitter releases a
strong acid only (dashed lines), and when the transmitter releases a strong
acid followed by base 0.5 second later (solid lines).
important benefits of the proposed system could be in reducing
the ISI.
As can be seen from Figure 2 the system response when
hydrogen ions (i.e. strong acid) are transmitted by the sender
can be very wide, with long tails. One strategy for removing
the tail is to transmit hydroxide ions (i.e. strong base) after the
acid transmission. Note that for two consecutive transmissions,
the simplified approximations that were presented in the previous section (i.e. no reaction assumption, or the assumption
that the reactions occur only at the receiver) cannot be applied
to the second transmission since the concentration of ions
in the channel will be high due to the initial transmission.
Therefore, only numerical evaluation is possible in this case.
The approximate models from previous section, however,
could be used in setting the initial conditions for the second
transmission.
In the last section it was shown that (16) plus 10−7 is a good
approximation for the initial acid transmission. For a constant
value of time T > 0, (17) as a function of spatial location `
is a Gaussian probability density function with mean vT and
variance 2DT . Therefore, the initial condition that represents
an acid transmission followed by a base transmission T
seconds later is given by
CH (x, t = 0) = NH N (vT, 2Da T ) + 10−7 ,
kw
COH (x, t = 0) = NOH δ(x) +
,
CH (x, t = 0)
(22)
(23)
where N (µ, σ 2 ) is the Gaussian probability density function
with mean µ and variance σ 2 . For numerical evaluations,
instead of the delta function the Gaussian probability density
function is used. Note that the same technique could be used to
model a base transmission followed by an acid transmission.
First, consider the case when an acid impulse is transmitted
followed by a base impulse. Figure 4 shows the results
when the separation distance between the transmitter and the
receiver is 900µm. It is assumed that T = 0.5 seconds,
NH = 0.001 moles, and NOH = 0.001005 moles. The
number of hydroxide ions released is larger to compensate
System Response to Base-Acid Tx at 9007m
Normalized Hydrogen Ion Concentration
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
Base-Acid Tx `=9007m, v=0
Acid Tx `=9007m, v=0
Base-Acid Tx `=9007m, v=107m/s
Acid Tx `=9007m, v=107m/s
Base-Acid Tx `=9007m, v=507m/s
Acid `=9007m, v=507m/s
0.2
0.1
0
0
50
100
150
200
Time (s)
Fig. 5. The system response at 900µm when the transmitter releases a
strong acid only (dashed lines), and when the transmitter releases a strong
base followed by acid 1 second later (solid lines).
for the smaller diffusion coefficient, which results in a flatter
concentration curves. In these plots, the dashed lines represent
the case where only an acid impulse is transmitted and the
solid lines represent the case where an acid impulse is followed
by a base impulse 0.5 seconds later. The plots are normalized
by the peak’s maximum for easy comparison. As can be
seen, the width of the response is decreased significantly and
the tails drop quickly toward zero when an acid impulse is
followed by a base impulse. Therefore, this can significantly
reduce ISI. However, because of the chemical interactions,
this reduction in hydrogen ion concentration also means an
increase in hydroxide ion concentration, which could effect
future transmissions.
To further investigate this effect, the case when a base
impulse is transmitted followed by an acid impulse is considered next. Figure 5 shows the results when the separation
distance between the transmitter and the receiver is 900µm. It
is assumed that T = 1 seconds, NH = 0.001005 moles, and
NOH = 0.001005 moles. Again the plots are normalized, and
the dashed lines represent an acid impulse only and the solid
lines represent an acid impulse that follows a base impulse
1 second later. As can be seen in the plots, because of the
presence of hydroxide ions in the channel from the initial base
impulse, there is a delay in response. However, combining the
result from Figures 4 and 5 it is evident that there is still a
significant improvement in ISI. For example, for pure diffusion
(blue lines) there is about 50 seconds delay until the pulse
drops close to zero in Figures 4, and about 50 seconds of
delay for the next pulse from Figure 5. This combined 100
seconds delay value is much better than the case where only
strong acids are transmitted (dashed blue line).
VI. C ONCLUSIONS AND F UTURE W ORK
A new and novel concentration-modulated molecular communication scheme using acids, bases and hydrogen ion concentration has been presented. In this scheme, the information
can be modulated onto the concentration of hydrogen ions,
and this concentration can be controlled through the release
of acids and bases at the transmitter. The important benefit of
this scheme is that the concentration can be both increased and
decreased through transmissions by the sender. This enables
inter-symbol interference mitigation schemes as well as the
possibility to form a wide array of signal patterns which
may be beneficial for control, high-level modulation and
multiple access. Another important benefit of this work is the
availability of pH sensors at micro-scale and macro-scale for
detection, which makes this scheme practical.
As was shown, it is difficult to find analytical expressions
for the propagation scheme because of the chemical reactions
that result in nonlinear partial differential equations. In the
future, we will further study this communication scheme by
using stochastic reaction-diffusion simulators, and building an
experimental platform. Moreover, we will explore the possibility of forming different signal patterns such as orthogonal
signals. Finally, we will consider the case where the transmitter
uses a weak acid and a weak base. The weak acids and bases
do not dissociate completely in water, and as a result their
corresponding model can be more complicated.
R EFERENCES
[1] N. Farsard, A. Yilmaz, H. B.and Eckford, C.-B. Chae, and W. Guo, “A
comprehensive survey of recent advancements in molecular communication,” arXiv:1410.4258v2, Oct. 2014.
[2] N. Farsad, A. W. Eckford, and S. Hiyama, “Channel design and
optimization of active transport molecular communication,” in Proc.
Int. Conf. on Bio-Inspired Models of Netw., Inf. and Comput. Syst.
(BIONETICS), York, England, 2011.
[3] M. U. Mahfuz, D. Makrakis, and H. T. Mouftah, “On the characterization of binary concentration-encoded molecular communication in
nanonetworks,” Nano Commun. Netw., vol. 1, no. 4, pp. 289–300, Dec.
2010.
[4] N.-R. Kim and C.-B. Chae, “Novel modulation techniques using isomers as messenger molecules for nano communication networks via
diffusion,” IEEE J. Sel. Areas Commun., vol. 31, no. 12, pp. 847–856,
Dec. 2013.
[5] N. Farsad, W. Guo, C.-B. Chae, and A. W. Eckford, “Stable Distributions
as Noise Models for Molecular Communication,” in Proc. IEEE Glob.
Commun. Conf. (GLOBECOM), 2015, to appear.
[6] M. S. Kuran, H. B. Yilmaz, T. Tugcu, and I. F. Akyildiz, “Modulation
techniques for communication via diffusion in nanonetworks,” in Proc.
IEEE Int. Conf. on Commun. (ICC), June 2011, pp. 1–5.
[7] N. Farsad, W. Guo, and A. W. Eckford, “Tabletop molecular communication: Text messages through chemical signals,” PLoS ONE, vol. 8,
no. 12, p. e82935, Dec. 2013.
[8] D. Kilinc and O. B. Akan, “Receiver design for molecular communication,” IEEE J. Sel. Areas Commun., vol. 31, no. 12, pp. 705–714, Dec.
2013.
[9] A. Noel, K. Cheung, and R. Schober, “Improving receiver performance
of diffusive molecular communication with enzymes,” IEEE Trans.
NanoBiosci., vol. 13, no. 1, pp. 31–43, March 2014.
[10] N. J. Tro, Principles of Chemistry: A Molecular Approach, 1st ed.
Upper Saddle River, NJ: Prentice Hall, Jan. 2009.
[11] J. Zhuang, R. Wright Carlsen, and M. Sitti, “pH-Taxis of Biohybrid
Microsystems,” Scientific Reports, vol. 5, p. 11403, Jun. 2015.
[12] M. L. Donten, J. VandeVondele, and P. Hamm, “Speed limits for acid–
base chemistry in aqueous solutions,” CHIMIA International Journal for
Chemistry, vol. 66, no. 4, pp. 182–186, 2012.
[13] R. Chang, Physical Chemistry for the Biosciences, 1st ed. Sansalito,
Calif: University Science Books, Jan. 2005.
[14] R. LeVeque, Finite Difference Methods for Ordinary and Partial Differential Equations: Steady-State and Time-Dependent Problems. Philadelphia, PA: SIAM, Jul. 2007.
[15] P. Atkins and J. de Paula, Physical Chemistry, 9th ed. New York: W.
H. Freeman, Dec. 2009.